Three Small Universal Turing Machines

  • Claudio Baiocchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2055)


We are interested by “small” Universal Turing Machines (in short: UTMs), in the framework of 2, 3 or 4 tape—symbols. In particular:
  • tape—symbols. Apart from the old 24—states machine constructed by Rogozhin in 1982, we know two recent examples requiring 22 states, one due to Rogozhin and one to the author.

  • tape—symbols. The best example we know, due to Rogozhin, requires 10 states. It uses a strategy quite hard to follow, in particular because even—length productions require a different treatment with respect to odd—length ones.

  • tape—symbols. The best known machines require 7 states. Among them, the Rogozhin’s one require only 26 commands; the Robinson’s one, though requiring 27 commands, fournishes an easier way to recover the output when the TM halts. In particular, Robinson asked for a 7 × 4 UTM with only 26 commands and an easy treatment of the output.

Here we will firstly construct a 7 × 4 UTM with an easy recover of the output which requires only 25 commands; then we will simulate such a machine by a (simple) 10 × 3 UTM and by a 19 × 2 UTM.


Turing Machine Digit Symbol Initial Letter Variable Length Code Universal Turing Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Claudio Baiocchi
    • 1
  1. 1.Dipartimento di MatematicaUniversità “La Sapienza” di RomaItaly

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